Curve fitting (polyfit, fit) in MATLAB - Mini Project: Build & Apply

Curve fitting with polyfit and fit in MATLAB

📖 Scenario: You are working as a data analyst. You have collected some measurements of temperature and ice cream sales. You want to find a simple curve that best matches the data points to understand the trend.

🎯 Goal: Build a MATLAB script that fits a straight line to the data points using polyfit and fit functions, then display the fitted line.

📋 What You'll Learn

Create vectors for temperature and sales data

Create a variable for the degree of the polynomial fit

Use polyfit to find the coefficients of the best fit line

Use fit function to fit a linear model

Plot the original data and the fitted line

Display the coefficients and the fit result

💡 Why This Matters

🌍 Real World

Curve fitting helps understand trends in data like sales, temperature, or scientific measurements.

💼 Career

Data analysts and engineers use curve fitting to model relationships and make predictions.

1

Create the data vectors

Create two vectors called temperature and sales with these exact values: temperature = [15, 18, 21, 24, 27, 30] and sales = [200, 220, 250, 270, 300, 320].

MATLAB

% Create vectors for temperature and sales data
% Your code here

Hint

Use square brackets to create vectors and separate values with commas.

2

Set the polynomial degree

Create a variable called degree and set it to 1 to indicate a linear fit.

MATLAB

temperature = [15, 18, 21, 24, 27, 30];
sales = [200, 220, 250, 270, 300, 320];
% Set the polynomial degree for fitting
% Your code here

Hint

Use a simple assignment to create the variable degree.

3

Fit the data using polyfit and fit

Use polyfit with temperature, sales, and degree to get coefficients in a variable called coeffs. Then use fit with temperature', sales', and 'poly1' to get a fit object called fitresult.

MATLAB

temperature = [15, 18, 21, 24, 27, 30];
sales = [200, 220, 250, 270, 300, 320];
degree = 1;
% Use polyfit to find coefficients
% Use fit to get a fit object
% Your code here

Hint

Remember to transpose vectors for fit using '.

4

Display and plot the results

Use disp to show coeffs and fitresult. Then plot temperature vs sales as points and overlay the fitted line using plot with temperature and polyval(coeffs, temperature). Add a legend and labels.

MATLAB

temperature = [15, 18, 21, 24, 27, 30];
sales = [200, 220, 250, 270, 300, 320];
degree = 1;
coeffs = polyfit(temperature, sales, degree);
fitresult = fit(temperature', sales', 'poly1');
% Display coefficients and fitresult
% Plot data points and fitted line
% Your code here

Hint

Use disp to show variables and plot to draw points and lines. Use hold on and hold off to combine plots.

Practice

1. What does the MATLAB function polyfit(x, y, n) do?

easy

A. It returns a fit object that can be used to predict new values.

B. It plots the data points x and y on a graph.

C. It finds the coefficients of a polynomial of degree n that fits the data points x and y.

D. It calculates the correlation coefficient between x and y.

Solution

1. Step 1: Understand the purpose of polyfit

   polyfit calculates polynomial coefficients that best fit the data points given by x and y.

2. Step 2: Differentiate from other functions

   Unlike fit, polyfit returns just coefficients, not a fit object or plot.

3. Final Answer:

   It finds the coefficients of a polynomial of degree n that fits the data points x and y. -> Option C

4. Quick Check:

   polyfit = polynomial coefficients [OK]

Hint: Remember: polyfit returns coefficients, fit returns a fit object [OK]

Common Mistakes:

• Confusing polyfit with fit function
• Thinking polyfit plots data
• Assuming polyfit returns a fit object

2. Which of the following is the correct syntax to fit a quadratic polynomial to data vectors x and y using polyfit?

easy

A. p = polyfit(x, y, 2);

B. p = polyfit(y, x, 2);

C. p = polyfit(x, y, 3);

D. p = polyfit(x, 2, y);

Solution

1. Step 1: Identify correct argument order

   The syntax is polyfit(x, y, n) where n is the polynomial degree.

2. Step 2: Confirm degree for quadratic

   Quadratic means degree 2, so the third argument must be 2.

3. Final Answer:

   p = polyfit(x, y, 2); -> Option A

4. Quick Check:

   polyfit(x, y, 2) fits quadratic [OK]

Hint: Remember order: x, y, degree in polyfit [OK]

Common Mistakes:

• Swapping x and y arguments
• Using wrong polynomial degree
• Incorrect argument order

3. What is the output of the following MATLAB code?

x = [1 2 3 4 5];
y = [2.2 4.1 6.0 8.1 10.2];
p = polyfit(x, y, 1);
y_fit = polyval(p, 6);

medium

A. y_fit = 12.1

B. y_fit = 12.3

C. y_fit = 13.0

D. y_fit = 10.2

Solution

1. Step 1: Fit a line to data

   Using polyfit with degree 1 fits a line y = mx + b to points.

2. Step 2: Calculate predicted value at x=6

   Using polyval, we evaluate the fitted line at x=6. The slope and intercept from polyfit give approximately y_fit = 12.1.

3. Final Answer:

   y_fit = 12.1 -> Option A

4. Quick Check:

   polyval(polyfit(x,y,1),6) ≈ 12.1 [OK]

Hint: polyval evaluates polynomial at given x [OK]

Common Mistakes:

• Confusing polyfit output with predicted value
• Using wrong degree in polyfit
• Calculating y_fit without polyval

4. Identify the error in this MATLAB code snippet for fitting data with fit:

x = (1:5)';
y = [2 4 6 8 10]';
f = fit(x, y, 'poly2');

medium

A. The fit type string should be 'poly1' for linear fit, not 'poly2'.

B. The fit function requires the Curve Fitting Toolbox to be installed.

C. The input vectors x and y must be row vectors, not column vectors.

D. The syntax is correct; there is no error.

Solution

1. Step 1: Check syntax and input shapes

   Vectors x and y as column vectors are valid inputs for fit.

2. Step 2: Verify toolbox requirement

   The fit function requires the Curve Fitting Toolbox; without it, the code will error.

3. Final Answer:

   The fit function requires the Curve Fitting Toolbox to be installed. -> Option B

4. Quick Check:

   fit needs toolbox installed [OK]

Hint: fit needs Curve Fitting Toolbox installed [OK]

Common Mistakes:

• Assuming fit works without toolbox
• Confusing poly1 and poly2 as errors
• Thinking vector orientation causes error

5. You have noisy data vectors x and y. You want to fit a cubic polynomial and then predict the value at x = 7. Which sequence of MATLAB commands correctly does this?

hard

A. p = polyfit(x, y, 3); y_pred = p(7);

B. f = fit(x, y, 'poly2'); y_pred = feval(f, 7);

C. p = polyfit(y, x, 3); y_pred = polyval(p, 7);

D. f = fit(x, y, 'poly3'); y_pred = feval(f, 7);

Solution

1. Step 1: Choose correct fit function and degree

   Using fit with 'poly3' fits a cubic polynomial to x and y.

2. Step 2: Predict value at x=7 using fit object

   Use feval(f, 7) or f(7) to get predicted y value from the fit object.

3. Final Answer:

   f = fit(x, y, 'poly3'); y_pred = feval(f, 7); -> Option D

4. Quick Check:

   fit with 'poly3' and feval predicts y at 7 [OK]

Hint: Use fit with 'poly3' and feval to predict [OK]

Common Mistakes:

• Swapping x and y in polyfit
• Using wrong polynomial degree
• Using poly2 instead of poly3 for cubic fit